Let $f(x)=x \cdot\left[\frac{x}{2}\right]$ for $-10
JEE MainMathematicsEasy
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QJEE MAIN 2020
The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word...
JEE MainMathematicsEasy
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QJEE MAIN 2020
The natural number m , for which the coefficient of $x$ in the binomial expansion of $\left(x^m+\frac{1}{x^2}\right)^{22}$ is 1540 , is $\_\_\_\_$ .
JEE MainMathematicsMedium
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Q JEE MAIN 2020
If the line, $2 x-y+3=0$ is at a distance $\frac{1}{\sqrt{5}}$ and $\frac{2}{\sqrt{5}}$ from the lines $4 x-2 y+\alpha=0$ and $6 x-3 y+\beta=0$, respectively, then the...
JEE MainMathematicsEasy
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QJEE MAIN 2020
Four fair dice are thrown independently 27 times. Then the expected number of times, at least two dice show up a three or a five,...
JEE MainMathematicsMedium
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QJEE MAIN 2020
If the volume of a parallelopiped, whose coterminus edges are given by the vectors $\vec{a}=\hat{i}+\hat{j}+n \hat{k}, \vec{b}=2 \hat{i}+4 \hat{j}-n \hat{k}$ and $...
JEE MainMathematicsMedium
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QJEE MAIN 2020
If the point $P$ on the curve, $4 x^2+5 y^2=20$ is farthest from the point $\mathrm{Q}(0,-4)$, then $\mathrm{PQ}^2$ is equal to :
JEE MainMathematicsEasy
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QJEE MAIN 2020
The product of the roots of the equation $9 x^2-18 |x|+5=0$, is :
JEE MainMathematicsEasy
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Q JEE MAIN 2020
If $2^{10}+2^9 \cdot 3^1+2^8 \cdot 3^2+\ldots .+2 \cdot 3^9+3^{10}=S-2^{11}$, then $S$ is equal to:
JEE MainMathematicsEasy
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QJEE MAIN 2019
An electromagnetic wave is represented by the electric field $\overrightarrow{\mathbf{E}}=\mathrm{E}_0 \hat{n} \sin [\omega t+(6 y-8 z)]$. Taking unit vectors in $x, y$ and $z$ directions...
JEE MainPhysicsHard
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Q JEE MAIN 2020
A survey shows that 73% of the persons working in an office like coffee, whereas 65% like tea. If x denotes the percentage of them,...
JEE MainMathematicsMedium
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QJEE MAIN 2020
If the minimum and the maximum values of the function $f: f:\left[\frac{\pi}{4}, \frac{\pi}{2}\right] \rightarrow R$, defined by $$ f(\theta)=\left|\begin{array}{ccc} -\sin ^2 \theta & -1-\sin ^2...
JEE MainMathematicsMedium
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QJEE MAIN 2019
$$
\text { The correct order of the oxidation states of nitrogen in NO, N2O, NO2, and N2O3 is }
$$
JEE MainChemistryEasy
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QJEE MAIN 2020
If $\alpha$ is the positive root of the equation, $p(x)=x^2-x -2=0$, then $\lim _{x \rightarrow \alpha^{+}} \frac{\sqrt{1-\cos (p(x))}}{x+\alpha-4}$ is equal to :
JEE MainMathematicsMedium
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QJEE MAIN 2019
A magnetic compass needle oscillates 30 times per minute at a place where the dip is $45^{\circ}$, and 40 times per minute where the dip...
JEE MainPhysicsEasy
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QJEE MAIN 2020
If the four complex numbers $z, \bar{z}, \bar{z}-2 \operatorname{Re}(\bar{z})$ and $z-2 \operatorname{Re}(z)$ represent the vertices of a square of side 4 units in the Argand...
JEE MainMathematicsHard
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QJEE MAIN 2019
The element having greatest difference between its first and second ionization energies, is
JEE MainChemistryEasy
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QJEE MAIN 2019
A point dipole $\hat{p}=-p_0 \hat{x}$ is kept at the origin. The potential and electric field due to this dipole on the $y$-axis at a distance...
JEE MainPhysicsMedium
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QJEE MAIN 2020
The mean and variance of 7 observations are 8 and 16, respectively. If five observations are 2, 4, 10, 12, 14, then the absolute difference...
JEE MainMathematicsHard
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QJEE MAIN 2020
If $3^{2 \sin 2 \alpha-1}, 14$ and $3^{4-2 \sin 2 \alpha}$ are the first three terms of an A.P. for some $\alpha$, then the sixth...
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